THE GLOBAL EXISTENCE OF BV SOLUTIONS OF THE ISENTROPIC p-SYSTEM WITH LARGE INITIAL DATA

In this paper,we study the global existence of BV solutions of the initial value problem for the isentropic p-system,where the state equation of the gas is given by P=Av-γ.For γ> 1,the general existence result for large initial data has not been obtained.By using the Glimm scheme,Nishida,Smoller and Diperna successively obtained the global existence results for(γ-1)TV(v0(x),u0(x)) being small.In the present paper,by adopting a rescaling technique,we improve these results and obtain the global existence result under the condition that(γ-1)γ+1(TV(v0(x)))γ-1(TV(u0(x)))2is small,which implies that,for fixed γ> 1,either TV(v0(x)) or TV(u0(x)) can be arbitrarily large.